Chapter 7.7, Problem 27PPS

To determine

To calculate: The total amount to the nearest cent.

Answer to Problem 27PPS

The total amount is $15496.72.

Explanation of Solution

Given information: The principal amount is $14,750, rate of compound interest is 5%, number of year = 1. The interest is compounded twice a year.

Formula used: The compound interest formula is $A=P{(1+\frac{r}{n})}^{nt}$

Where, A = Total amount including interest, P = principal amount, r =annual rate of interest, n = number of compounding periods, t = the number of years.

Calculation:

In the problem given,

P = $14,750, r = $5\%=\frac{5}{100}=0.05$ , n = 2, t =1year

  $\begin{array}{}$ A=P{(1+\frac{r}{n})}^{nt}$$ \Rightarrow A=14750{(1+\frac{0.05}{2})}^{2\times 1}$$ \Rightarrow A=14750{(1+0.025)}^2$$ \Rightarrow A=14750{(1.025)}^2$$ \Rightarrow A=14750(1.050625)$$ \Rightarrow A=\text{15496}\text{.71875}$$ \Rightarrow A=\text{15496}\text{.72}$\end{array}$

The total amount is $15,496.72.